Unit 2  Objective 3  Division of Polynomials
You may need to review Unit 1  Objective 4
 Rules of Exponents again. Remember (a^{m}) / (a^{n}) = a^{m
 n}.
(In #1 the denominator should have x raised to the 2nd power)
Examples:

To divide a polynomial by a mononomial, divide each term of the
polynomial by the mononomial.
Examples:
1. 



2. 
NOTE: (#2 has some mistakes  numerator of the 1st line should be 3xy not 6xy
2nd line the numerator of the first term should be 3xy not 6xy
3rd line the first term should be 1 not 3 and the second term constant should
be 4/3 not 4
4th line the first term should be 1 not 3 and the second term should be (4/3)y not 4y 

To divide a polynomial by a polynomial follow these steps:
 Write both the dividend and the divisor in decreasing order of
powers.
 Are there any missing terms? If there are then write a coefficient of
0.
 Set up the problem as long division.
 Divide the first term in the dividend by the first term in the
divisor.
 Multiply the divisor by this first term of the quotient. Write the
product below the dividend with like terms under like terms. Subtract the product from the
dividend.
 Repeat the last two steps until the power of the new dividend is less
than the power of the divisor.
Examples:
1. Divide 6x^{2}  4
 4x + 8x^{4} by 2x + 1
This first term in the dividend is 8x^{4} and
the first term in the divisor is 2x. You would say 2x times what would give you 8x^{4}
and you answer would be 4x^{3}.
2. Divide
4x^{5}  2x^{3} + 6x^{2}  8 by (4x^{2}
+ 2)

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